1217 
Hence it follows, therefore, that Zp and £' cannot be converted 
into one another; as we are able to deduce this in the same way 
for Hr and MZ" and also for /' and #", the property mentioned 
sub- a is proved. At the same time it appears from the deduction 
that it need not be true for equilibria in unstable condition. 
For the equilibria Z' and £" this property follows also at once 
without calculation viz. from the condition that under constant P 
and at constant 7’ & must be a minimum. 
The properties, mentioned sub 6 and c follow now at once from 
property a and formula (20). 
Leiden, Inorg. Chem. Lab. (To be continued), 
Mechanics. — “On the relativity of mertia. Remarks concerning 
Einstein's latest hypothesis’ *) By Prof. W. DE SITTER. 
(Communicated in the meeting of March 31, 1917). 
If we neglect the gravitational action of all ordinary matter (sun, 
stars, etc.), and if we use as a system of reference three rectangular 
cartesian space-coordinates and the time multiplied by ec, then in 
that - part of the four-dimensional time-space which is accessible to 
our observations, the g,, are very approximately those of the old 
theory of relativity, viz.: 
—l 0 0 0 
0 —l 0 0 
0 0 -1 0 
0 0 0 +1 
The part of the time-space where this is so, I shall call “our 
neighbourhood”. In space this extends at least to the farthest star, 
nebula or cluster in whose spectrum we can identify definite lines ®). 
How the g,, are outside our neighbourhood we do not know, 
and any assumption regarding their values is an extrapolation, whose 
uncertainty increases with the distance (in space, or in time, or in 
both) from the origin. How the g,, are at infinity of space or of 
time, we will never know. Nevertheless the need has been felt to 
eae Be an EE) 
1) A. Einstein, Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, 
Sitzungsber. Berlin, 8 Febr. 1917, page 142. 
2) W. pe Sitter, On Ernstern’s theory of gravitation and its astronomical con- 
sequences (second paper), Monthly Notices R.A.S. Dec. 1916, Vol. LX XVII, p. 182. 
This limit refers to g44 only. 
